Phase-space representations based on coherent states ($P$,$Q$, Wigner) have been successful in the creation of stochastic differential equations (SDEs) for the efficient stochastic simulation of high-dimensional quantum systems. However, many problems using these techniques remain intractable over long integration times. We present a number-phase Wigner representation that can be unraveled into SDEs. We demonstrate convergence to the correct solution for an anharmonic oscillator with small dampening for significantly longer than other phase-space representations. This process requires an effective sampling of a nonclassical probability distribution. We describe and demonstrate a method of achieving this sampling using stochastic weights.

The second-order Zeeman effect of the sodium clock transition in a weak magnetic field of less than 50 $\mu$T was measured as the scalar Aharonov-Bohm phase by two-photon stimulated Raman atom interferometry. The ac Stark effect of the Raman pulse was canceled out by adopting an appropriate intensity ratio of two photons in the Raman pulse. The Ramsey fringes for the pulse separation of 7 ms were obtained with a phase uncertainty of $\pi /$200 rad. The nondispersive feature of the scalar Aharonov-Bohm phase was clearly demonstrated through 18 fringes with constant amplitude. The Breit-Rabi formula of the sodium clock transition was verified to be $\Delta \nu =(0.222\pm 0.003)\times {10}^{12}\times B^{1.998\pm 0.004}$ in a magnetic field of less than 50 $\mu$T.

We propose a concatenated cranking approach to resolve the dynamics for a class of time-dependent quantum systems with specific algebraic structure. By invoking a series of canonical transformations successively, concatenated representation of the Schrödinger equation is established and evolution of the system is solved in the cranking representation via discarding high-order nonadiabatic terms. The introduced method is then applied to investigate nonadiabatic dynamics and imperfection effects in pulsed gate operations of quantum dot systems regarding the existence of spin-orbit effects. The fidelity loss of the SWAP gate owing to anisotropic exchange and the fidelity retrieval of the Loss-DiVincenzo pulse sequence under nonadiabatic evolution are elaborated by virtue of the proposed method.

We have calculated the lowest-order relativistic effects for the three lowest states of the helium atom with symmetry ${}^{1}S$, ${}^{1}P$, ${}^{1}D$, ${}^{3}S$, ${}^{3}P$, and ${}^{3}D$ using variational Monte Carlo methods and compact, explicitly correlated trial wave functions. Our values are in good agreement with the best results in the literature.

Using a multiple-scale asymptotic approach, we have derived the complex cubic Ginzburg-Landau equation for amplified and nonlinearly saturated surface plasmon polaritons propagating and diffracting along a metal-dielectric interface. An important feature of our method is that it explicitly accounts for nonlinear terms in the boundary conditions, which are critical for a correct description of nonlinear surface waves. Using our model we have analyzed filamentation and discussed the bright and dark spatially localized structures of plasmons.

A scheme is presented for entangling the atoms of an optical lattice to reduce the quantum projection noise of a clock measurement. The divalent clock atoms are held in a lattice at a “magic” wavelength that does not perturb the clock frequency—to maintain clock accuracy—while an open-shell $J=1/2$ “head” atom is coherently transported between lattice sites via the lattice polarization. This polarization-dependent “Archimedes’ screw” transport at magic wavelength takes advantage of the vanishing vector polarizability of the scalar, $J=0$, clock states of bosonic isotopes of divalent atoms. The on-site interactions between the clock atoms and the head atom are used to engineer entanglement and for clock readout.

Theoretical and experimental fully differential cross sections are presented for electron-impact ionization of molecular hydrogen in a plane perpendicular to the incident beam direction. The experimental data exhibit a maximum for $1$-eV electrons detected ${180}^{°}$ apart and a minimum for $10$-eV electrons. We investigate the different physical effects which cause back-to-back scattering and demonstrate that, over the energy range from $10$ to $1$ eV, a direct transition is observed from a region where Wannier threshold physics is essentially unimportant to where it completely dominates.

We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped ${}^{87}\mathrm{Rb}$ atoms. Recent progress in metrology exploits so-called magic wavelengths, whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkali metals due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically trapped neutral atoms.

We analyze experimentally the dynamics of optical patterns emerging from a photorefractive two-wave mixing geometry where a tilted single-feedback mirror generates an advectionlike effect. Depending on the nonlocal coupling (introduced by the tilting angle) between the two counterpropagating beams, the strength of the nonlocal response of the nonlinear photorefractive bulk medium, and the distance between the mirror and the crystal, we observe the initiation of different pattern geometries, the inversion of pattern transverse phase velocity, and the bifurcation from convective to absolute instabilities.

We consider the high-gain spontaneous parametric down-conversion in a noncollinear geometry as a paradigmatic scenario to investigate the quantum-to-classical transition by increasing the pump power, that is, the average number of generated photons. The possibility of observing quantum correlations in such a macroscopic quantum system through dichotomic measurement will be analyzed by addressing two different measurement schemes, based on different dichotomization processes. More specifically, we will investigate the persistence of nonlocality in an increasing size $\frac{n}{2}$-spin singlet state by studying the change in the correlations form as $n$ increases, both in the ideal case and in presence of losses. We observe a fast decrease in the amount of Bell’s inequality violation for increasing system size. This theoretical analysis is supported by the experimental observation of macro-macro correlations with an average number of photons of about ${10}^3$. Our results shed light on the practical extreme difficulty of observing nonlocality by performing such a dichotomic fuzzy measurement.

A $2\otimes 2$ unitary operation is called a perfect entangler if it can generate a maximally entangled state from some unentangled input. We study the following question: How many runs of a given two-qubit entangling unitary operation are required to simulate some perfect entangler with one-qubit unitary operations as free resources? We completely solve this problem by presenting an analytical formula for the optimal number of runs of the entangling operation. Our result reveals an entanglement strength of two-qubit unitary operations.

We study the local distinguishability of general multiqubit states and show that local projective measurements and classical communication are as powerful as the most general local measurements and classical communication. Remarkably, this indicates that the local distinguishability of multiqubit states can be decided efficiently. Another useful consequence is that a set of orthogonal $n$-qubit states is locally distinguishable only if the summation of their orthogonal Schmidt numbers is less than the total dimension $2^n$. Employing these results, we show that any orthonormal basis of a subspace spanned by arbitrary three-qubit orthogonal unextendible product bases (UPB) cannot be exactly distinguishable by local operations and classical communication. This not only reveals another intrinsic property of three-qubit orthogonal UPB but also provides a class of locally indistinguishable subspaces with dimension $4$. We also explicitly construct locally indistinguishable subspaces with dimensions $3$ and $5$, respectively. Similar to the bipartite case, these results on multipartite locally indistinguishable subspaces can be used to estimate the one-shot environment-assisted classical capacity of a class of quantum broadcast channels.

Quantum squeezing, an irreducible resource for quantum communication and quantum metrology, is very fragile and can be lost due to classical noise produced by an environment. We show that a classical correlation between the squeezed signal and the classical probe partially monitoring noise from the environment can be used as a resource to restore the lost squeezing. Two basic methods, the feed-forward restoration and the unitary decoupling, are proposed to exploit this classical correlation. They are mutually compared for high and low squeezing and also in the different regimes of correlated classical noise. On one side, a robustness against classical probe noise to restore at least nonzero squeezing is discussed, and on the other side, a complete revealing of the high squeezing by a squeezed probe and unitary decoupling is proposed.

We show that finding the lowest eigenvalue of a $3$-local symmetric stochastic matrix is Quantum-Merlin-Arthur-complete (QMA-complete). We also show that finding the highest energy of a stoquastic Hamiltonian is QMA-complete and that adiabatic quantum computation using certain excited states of a stoquastic Hamiltonian is universal. We also show that adiabatic evolution in the ground state of a stochastic frustration-free Hamiltonian is universal. Our results give a QMA-complete problem arising in the classical setting of Markov chains and adiabatically universal Hamiltonians that arise in many physical systems.

Employing the quantum Rényi $\alpha$ entropies as a measure of entanglement, we numerically find the violation of the strong superadditivity inequality for a system composed of four qubits and $\alpha >1$. This violation gets smaller as $\alpha \to 1$ and vanishes for $\alpha =1$ when the measure corresponds to the entanglement of formation. We show that the Rényi measure aways satisfies the standard monogamy of entanglement for $\alpha =2$, and only violates a high-order monogamy inequality, in the rare cases in which the strong superadditivity is also violated. The sates numerically found where the violation occurs have special symmetries where both inequalities are equivalent. We also show that every measure satisfying monogamy for high-dimensional systems also satisfies the strong superadditivity inequality. For the case of Rényi measure, we provide strong numerical evidences that these two properties are equivalent.

Covariance matrices are a useful tool for investigating correlations and entanglement in quantum systems. They are widely used in continuous-variable systems, but recently also for finite-dimensional systems powerful entanglement criteria in terms of covariance matrices have been derived. We show how these results can be used for the quantification of entanglement in bipartite systems. To that aim we introduce an entanglement parameter that quantifies the violation of the covariance matrix criterion and can be used to give lower bounds on the concurrence. These lower bounds are easily computable and give entanglement estimates for many weakly entangled states.

The characterization of an infinite-order quantum phase transition (QPT) by entanglement measures is analyzed. To this aim, we consider two closely related solvable spin-1/2 chains, namely, the Ashkin-Teller and the staggered $\mathit{XXZ}$ models. These systems display a distinct pattern of eigenstates but exhibit the same thermodynamics, that is, the same energy spectrum. By performing exact diagonalization, we investigate the behavior of pairwise and block entanglement in the ground state of both models. In contrast with the $\mathit{XXZ}$ chain, we show that pairwise entanglement fails in the characterization of the infinite-order QPT in the Ashkin-Teller model, although it can be achieved by analyzing the distance of the pair state from the separability boundary. Concerning block entanglement, we show that both $\mathit{XXZ}$ and Ashkin-Teller models exhibit identical von Neumann entropies as long as a suitable choice of blocks is performed. Entanglement entropy is then shown to be able to identify the quantum phase diagram, even though its local extremes (either maximum or minimum) may also appear in the absence of any infinite-order QPT.

The full Dicke model is composed of a single bosonic mode and an ensemble of $N$ identical two-level atoms. In the model, the coupling between the bosonic mode and the atoms generates resonant and nonresonant processes. We also consider a dipole-dipole interaction between the atoms, which is able to generate entangled states in the atomic system. By assuming thermal equilibrium with a reservoir at temperature ${\beta }^{-1}$, the transition from fluorescent to superradiant phase and the quantum phase transition are investigated. It is shown that the critical behavior of the full Dicke model is not modified by the introduction of the dipole-dipole interaction.

Recent results suggest that the use of ensembles in statistical mechanics may not be necessary for isolated systems, since typically the states of the Hilbert space would have properties similar to those of the ensemble. Nevertheless, it is often argued that most of the states of the Hilbert space are nonphysical and not good descriptions of realistic systems. Therefore, to better understand the actual power of typicality it is important to ask if it is also a property of a set of physically relevant states. Here we address this issue, studying if and how typicality emerges in the set of matrix product states. We show analytically that typicality occurs for the expectation value of subsystems’ observables when the rank of the matrix product state scales polynomially with the size of the system with a power greater than 2. We illustrate this result numerically and present some indications that typicality may appear already for a linear scaling of the rank of the matrix product state.

Momentum correlations in three-body predissociation of triatomic hydrogen are investigated by quasiclassical trajectory calculations. It is shown that nonadiabatic couplings that trigger predissociation of the $2{\mathit{sA}}_1^{\text{'}}$ state of ${\mathrm{H}}_3$ imprint their geometric properties on the momentum correlation structures observed after dissociation. A simple symmetry-based model of the geometric coupling properties succeeds in reproducing most of the experimentally observed patterns. The ground-state dynamics that transform the geometric properties of the coupling into the final momentum correlations are identified.